hot body radiation

Welcome to the forum, Modu.
The problem with your logic is that you are dividing the energy spectrum into infinitely many infinitely small frequency bands. When you do that, the energy in each band is infinitely small. When you add infinitely many infinitely small quantities, you can get a finite total. You'll learn all about that in first year calculus.

Black-body radiation is distributed on a bell-shaped curve, just like most random events. The energy per wave length is greatest at a given frequency, which is determined by the temperature. Above and below that frequency, the energy per wave length tapers off toward zero in both directions. The area under the curve is the total energy, and it is a finite value, even though the curve extends to infinity.

Are you talking about the "ultraviolet catastrophe", modu?

--Astro

TAHNKS FOR THE REPLY PHIL
i grasp the concept of many infinite quntities adding up to a finite quantity, but that isn't my problem with the logic.
my problem may arise from lack of knowledge (as i stated above), most of which coming from popular scince (such as steven hawkings - brief history of time and such), now while i'm not sure what credential he (steven hawkings) has on this board, i assume that generaly speaking his statement are correct.
in the above mentioned book he describe the ideas and concepts that lead to heisenberg "uncertainty principal", "plank constant" and "quntom mechanic", in the following manner (more or less)
1. its assumed that hot body such as a star radiate energy in all frequncies
2. since the number (or range) of frequncy is infinite the body should also radiate infinite energy
3. conclusion of number 2 is not allowed therfore the problem
4. plank sugested thet a hot body dosent radiate energy in arbitary manner but in small packet called "qunta" each qunta can have a limited amount of energy and so in higher frequncy there want be enogh energy to create a qunta and so the body will loose energy at a finite rate (i know that what i just described its not precise, but its outline the train of thoght more or less)
my problem with the logic is as follow:
1. why was it assumed that a hot body radiate energy in all frequncies to start with?
2. once that it was clear that the above mentioned assumption was not true, why wasnt it simply discarded
3. lets assume that we cannot discard of the assumption in number 1 for whatever reasons (which are unkown to me), there is much easier and simpler way to explaine it:
A HOT BODY RADIATE ENERGY AT ONLY ONE FREQUNCY AT ANY GIVEN MOMENT, AND WE AS PERCIVER DETECT IT AS INFINITE FREQUNCIES.
the reason that we detect infinite or large number of frequncies can be explaind by harmonies.
for example if we transmit an electronic pulse at 100MHZ we can detect it at 100MHZ, 99MHZ, 98MHZ AND SO ON.(we can also detect it at higher frequncies, depending on our detection method, or at least i think so, not sure about it)
assuming the above is correct, there is no reason for the "qunta" explanation.
ps
Astro i'm not familiar with the "ultraviolet catastrophe"





modu

The blackbody is an idealized model and not a real radiator somewhat like the Carnot Cycle is to real cycles. Maybe a look at LEDs might help here. The LED emits lots of energy at high frequency(light) but nothing is emited at other frequencys. All real emiters deveate from the ideal blackbody. But, it still is a good approximation if you don't overuse it. Knowing how to use tools should be learned along with what the limits of the tool is.

Hello Everyone

This is my first post. I would be considered a real amateur; I think with all this physics/math stuff here; however, i have long held intense interest in the general principles in a wide range of scientific topics; especially physics. A lot of the math stuff is quite foreign to me, but I really enjoy learning, so I appreciate finding this forum and being able to explore & study.

I would like to quote something I read in a post above, and then ask a question: <blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">2. since the number (or range) of frequncy is infinite the body should also <b>radiate infinite energy</b><hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I don't understand a statement like this, because I have understood that "infinite energy" would only be required for something to move at lightspeed. Therefore, how can anything emit infinite energy; unless it was to move this fast? Also, as far as I know, nothing can travel at lightspeed anyway; only "almost" at light speed would be possible? These questions make me wonder, just what is a "hotbody?"

Some of my questions might be quite elementary; but I really learn from them [8D] Thanks, in advance for your replies.

- why2day

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by why2day</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">[modu]: since the number (or range) of frequncy is infinite the body should also radiate infinite energy<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I don't understand a statement like this, because I have understood that "infinite energy" would only be required for something to move at lightspeed.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The quoted statement is false. Lots of things are composed of an infinite number of parts, yet have a finite sum or measure. Examples include a line segment (infinite points, finite length) and summation series (e.g., 1/2 + 1/4 + 1/8 + 1/16 + ... to infinity = 1.0 exactly). A "black body" (one that is in thermal equilibrium, where energy in equals energy out) radiates at all frequencies, but has only a finite total energy being radiated. The amounts radiated at most frequencies are insignificant, just as most of the terms in the summation series I mentioned are insignificant in the final sum.

Although the idea is slow to catch on, it is now published and undisputed in print that the speed of light is no longer some kind of universal speed limit. So many of the old ideas about its special place in physics are passe. A spacecraft traveling at that speed would not have infinite energy.

Think of a plane trying to fly faster than sound using propeller power only (no jet or gravity assist). One could pour infinite energy into spinning the propellers, but the plane could still not reach or exceed the speed of sound in air. Likewise, if we use only chemical and electromagnetic forces to accelerate a spacecraft (forces whose propagation speed is limited to the speed of light), even an infinite amount of energy supplied to the spacecraft could not get it to reach or exceed the speed of light. But if we use gravity (which propagates faster than light) to accelerate the spacecraft, the transition from sub-light speed to superluminal speed is as smooth as breaking the sound barrier. The counterpart to a "sonic boom" is called "Cherenkov radiation". -|Tom|-